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Information × Registration Number 0219U003212, 0116U001528 , R & D reports Title Monogenic functions in Banach algebras and boundary value problems of analysis and mathematical physics popup.stage_title Head Gerus Oleg Fedorovych, Кандидат фізико-математичних наук Registration Date 25-01-2019 Organization Zhytomyr State University named after Ivan Franko popup.description2 The method of reduction of boundary-value problems of the Schwarz type for monogenic functions associated with biharmonic potentials and boundary-value problems of the plane theory of elasticity to the integral equations of Fredholm is developed. A new method of solving linear differential equations with partial derivatives with constant coefficients is developed. A class of flat orthotropic bodies is found, for which each component of the vector-solution of the system of equations of the equilibrium of Lyme relative to the displacement vector satisfies the equation for the stress function. All bases of two-dimensional commutative algebras with one unit over a field of complex numbers are found, which are associated with equations of stress function for a certain class of orthotropic flat deformations. Problems are found for monogenic functions such as the Schwarz problem type, the so-called boundary (k-m) problems, to which the boundary value problems of a flat isotropic theory of elasticity are reduced, and a series of such problems is solved for m = 4. A new class of quaternion functions, analytic by Hausdorff, is introduced, and the relation between it and the known classes of quaternion differentiation functions is established. The relationship between the known quaternion derivative and the Hausdorff derivative is investigated. It is shown that each harmonic function is a component of a monogenic function with values in a topological vector space, which is a extension of some infinite-dimensional commutative associative Banach algebra associated with the three-dimensional Laplace equation. Operational equations for spatial potentials generated by a hypercomplex integral of Cauchy type are derived, and the formulas relating the point spectra of these potentials are proved. The logarithmic residue of monogenic functions in a commutative associative complex Banach algebra with one-dimensional radical is investigated and calculated. A constructive description of all G-monogenic maps with values in the complex quaternion algebra in terms of four corresponding analytic functions of a complex variable is established. The analogues of integral Cauchy theorems for surface and curvilinear integrals from G-monogenic maps with values in the algebra of complex quaternions, as well as analogs of the Cauchy integral formula, theorems of Morera, Taylor, and Laurent are proved. Product Description popup.authors Грищук Сергій Вікторович Кузьменко Тетяна Сергіївна Плакса Сергій Анатолійович Пухтаєвич Роман Петрович Шпаківський Віталій Станіславович popup.nrat_date 2020-04-02 Close